A volunteer project to improve extension management is under way, which will address at least part of this requirement (I am not sure that automatic updating will occur, given the complexity of working out which extensions are needed, but we will see.)

A repository would be great, but I think it would be even more effective to be able to keep within the project's Material folder the various extensions which are used in a game. This way it would be easier to work on a project from several machines.